AutoEFT: Automated operator construction for effective field theories

The program AutoEFT is described. It allows one to generate Effective Field Theories (EFTs) from a given set of fields and symmetries. Allowed fields include scalars, spinors, gauge bosons, and gravitons. The symmetries can be local or global Lie groups based on U (1) and SU (N). The mass dimension of the EFT is limited only by the available computing resources. The operators are stored in a compact, human and machine-readable format. Aside from the program itself, we provide input files for EFTs based on the Standard Model and a number of its extensions. These include additional particles and symmetries, EFTs with minimal flavor violation, and gravitons. Program title: AutoEFT CPC Library link to program files: https: //doi. org/10. 17632/z8xm2hpbsp. 1 Developer's repository link: https: //gitlab. com/autoₑft/autoeft Licensing provisions: MIT license Programming language: Python Nature of problem: The bottom-up construction of an Effective Field Theory (EFT) which describes physics below a certain energy scale Λ requires obtaining a set of operators, composed of fields with mass m≪Λ, that are invariant under certain symmetries. One is primarily interested in complete sets of independent operators, called operator bases. Their construction for a given mass dimension of the operators is nontrivial due to algebraic and kinematic relations that may render different operators redundant. Except for the lowest mass dimensions, the number of operators is so large that the task of constructing an explicit EFT operator basis requires a high degree of automation on a computer. In addition, an automated approach will allow one to immediately take into account newly postulated or discovered light particles beyond the Standard Model. Solution method: Based on the group theoretical techniques and concepts established in Refs. 1–9 and in particular Refs. 10, 11, we developed the program AutoEFT, capable of constructing a non-redundant on-shell operator basis for general EFTs and arbitrary mass dimension. Provided a suitable model file, the respective operator basis is generated explicitly, including contractions of the symmetry group indices, in a fully automated fashion. Due to the generality of the algorithm, it can be applied to a variety of low-energy scenarios. The underlying low-energy theory is encoded in a model file which defines the symmetries and the field content. The fairly simple format enables the user to compose their own model files and to construct the respective operator basis with minimal effort. Additional comments including restrictions and unusual features: In its current form, AutoEFT is restricted to theories including particles with spin 0, 1/2, 1, and 2, where the latter two are considered massless. In addition, AutoEFT only constructs operators that mediate proper interactions, meaning that any operator must be composed of at least three fields. The internal symmetries must be given as factors of U (1) and SU (N) groups. In principle, operator bases can be generated for any mass dimension, which is, however, limited by the available computing resources. Y. Shadmi, Y. Weiss, Effective field theory amplitudes the on-shell way: scalar and vector couplings to gluons, J. High Energy Phys. 02 (2019) 165, arXiv: 1809. 09644 hep-ph. B. Henning, T. Melia, Conformal-helicity duality & the Hilbert space of free CFTs, arXiv: 1902. 06747 hep-th. T. Ma, J. Shu, M. -L. Xiao, Standard model effective field theory from on-shell amplitudes, Chin. Phys. C 47 (2023) 023105, arXiv: 1902. 06752 hep-ph. B. Henning, T. Melia, Constructing effective field theories via their harmonics, Phys. Rev. D 100 (2019) 016015, arXiv: 1902. 06754hep-ph. R. Aoude, C. S. Machado, The Rise of SMEFT on-shell amplitudes, J. High Energy Phys. 12 (2019) 058, arXiv: 1905. 11433 hep-ph. R. M. Fonseca, Enumerating the operators of an effective field theory, Phys. Rev. D 101 (2020) 035040, arXiv: 1907. 12584 hep-ph. G. Durieux, T. Kitahara, Y. Shadmi, Y. Weiss, The electroweak effective field theory from on-shell amplitudes, J. High Energy Phys. 01 (2020) 119, arXiv: 1909. 10551 hep-ph. A. Falkowski, Bases of massless EFTs via momentum twistors, arXiv: 1912. 07865hep-ph. G. Durieux, C. S. Machado, Enumerating higher-dimensional operators with on-shell amplitudes, Phys. Rev. D 101 (2020) 095021, arXiv: 1912. 08827 hep-ph. H. -L. Li, Z. Ren, J. Shu, M. -L. Xiao, J. -H. Yu, Y. -H. Zheng, Complete set of dimension-eight operators in the standard model effective field theory, Phys. Rev. D 104 (2021) 015026, arXiv: 2005. 00008hep-ph. H. -L. Li, Z. Ren, M. -L. Xiao, J. -H. Yu, Y. -H. Zheng, Complete set of dimension-nine operators in the standard model effective field theory, Phys. Rev. D 104 (2021) 015025, arXiv: 2007. 07899 hep-ph.